What is the Greatest Common Factor of 18405 and 18414?

Greatest common factor (GCF) of 18405 and 18414 is 9.

GCF(18405,18414) = 9

We will now calculate the prime factors of 18405 and 18414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18405 and 18414.

How to find the GCF of 18405 and 18414?

We will first find the prime factorization of 18405 and 18414. After we will calculate the factors of 18405 and 18414 and find the biggest common factor number .

Step-1: Prime Factorization of 18405

Prime factors of 18405 are 3, 5, 409. Prime factorization of 18405 in exponential form is:

18405 = 3² × 5¹ × 409¹

Step-2: Prime Factorization of 18414

Prime factors of 18414 are 2, 3, 11, 31. Prime factorization of 18414 in exponential form is:

18414 = 2¹ × 3³ × 11¹ × 31¹

Step-3: Factors of 18405

List of positive integer factors of 18405 that divides 18405 without a remainder.

1, 3, 5, 9, 15, 45, 409, 1227, 2045, 3681, 6135

Step-4: Factors of 18414

List of positive integer factors of 18414 that divides 18405 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 27, 31, 33, 54, 62, 66, 93, 99, 186, 198, 279, 297, 341, 558, 594, 682, 837, 1023, 1674, 2046, 3069, 6138, 9207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18405 and 18414. The biggest common factor number is the GCF number.
So the greatest common factor 18405 and 18414 is 9.

Also check out the Least Common Multiple of 18405 and 18414